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{{redirect|OAEP|the division of the Thailand Ministry of Science Technology and Environment previously known as the Office of Atomic Energy for Peace|Office of Atoms for Peace}}
In [[cryptography]], '''Optimal Asymmetric Encryption Padding''' ('''OAEP''') is a [[padding (cryptography)|padding scheme]] often used together with [[RSA (cryptosystem)|RSA encryption]]. OAEP was introduced by [[Mihir Bellare|Bellare]] and [[Phillip Rogaway|Rogaway]],<ref>[[Mihir Bellare|M. Bellare]], [[Phillip Rogaway|P. Rogaway]]. ''Optimal Asymmetric Encryption -- How to encrypt with RSA''. Extended abstract in Advances in Cryptology
The OAEP algorithm is a form of [[Feistel network]] which uses a pair of [[random oracle]]s G and H to process the plaintext prior to [[asymmetric encryption]]. When combined with any secure [[trapdoor one-way function|trapdoor one-way permutation]] <math>f</math>, this processing is proved in the [[random oracle model]] to result in a combined scheme which is [[semantic security|semantically secure]] under [[chosen plaintext attack]] [[ciphertext indistinguishability|(IND-CPA)]]. When implemented with certain trapdoor permutations (e.g., RSA), OAEP is also proven to be secure against [[chosen ciphertext attack]]. OAEP can be used to build an [[all-or-nothing transform]].
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The original version of OAEP (Bellare/Rogaway, 1994) showed a form of "[[plaintext-aware encryption|plaintext awareness]]" (which they claimed implies security against [[chosen ciphertext attack]]) in the random oracle model when OAEP is used with any trapdoor permutation. Subsequent results contradicted this claim, showing that OAEP was only [[ciphertext indistinguishability|IND-CCA1]] secure. However, the original scheme was proved in the [[random oracle model]] to be [[ciphertext indistinguishability|IND-CCA2]] secure when OAEP is used with the RSA permutation using standard encryption exponents, as in the case of RSA-OAEP.<ref>
Eiichiro Fujisaki, Tatsuaki Okamoto, David Pointcheval, and [[Jacques Stern]]. ''RSA-- OAEP is secure under the RSA assumption''. In J. Kilian, ed., Advances in Cryptology
An improved scheme (called OAEP+) that works with any trapdoor one-way permutation was offered by [[Victor Shoup]] to solve this problem.<ref>
Victor Shoup. ''OAEP Reconsidered''. IBM Zurich Research Lab, Saumerstr. 4, 8803 Ruschlikon, Switzerland. September 18, 2001. [http://www.shoup.net/papers/oaep.pdf full version (pdf)]</ref>
More recent work has shown that in the [[Standard Model (cryptography)|standard model]] (that is, when hash functions are not modeled as random oracles) it is impossible to prove the IND-CCA2 security of RSA-OAEP under the assumed hardness of the [[RSA problem]].<ref>
P. Paillier and J. Villar, ''Trading One-Wayness against Chosen-Ciphertext Security in Factoring-Based Encryption'', Advances in Cryptology
D. Brown, [http://eprint.iacr.org/2006/223 ''What Hashes Make RSA-OAEP Secure?''], IACR ePrint 2006/233.</ref>
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